Results of Russian geomagnetic observatories in the 19th century: magnetic activity, 1841–1862

Hourly (spot readings) magnetic data (H- and D-components) were digitized from Russian yearbook tables for the years 1850–1862 from four observatories. The pdf pictures for digitization were taken by a normal digital camera. The database obtained consists of about 900 000 single data points. The time series of hourly magnetic values reveal slow secular variations (declination only) as well as transient and regular geomagnetic variations of external origin. The quality and homogeneity of the data is satisfactory. Daily Ak-indices were calculated using the index algorithm that has been earlier applied to 19th century data from Helsinki (Finland) as well as modern magnetic observatory recordings. The activity index series derived from the Russian data is consistent with earlier activity index series for 1850–1862. The digitized index data series derived in this study was extended back to 1841 by including magnetic <I>C</I>9 activity index data available from a Russian observatory (St. Petersburg). Magnetic data rescued here is well suitable for various reconstructions for studies of the long-term variation of the space weather in the 19th century

Quasi-periodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems

We consider a class of ordinary differential equations describing one-dimensional analytic systems with a quasi-periodic forcing term and in the presence of damping. In the limit of large damping, under some generic non-degeneracy condition on the force, there are quasi-periodic solutions which have the same frequency vector as the forcing term. We prove that such solutions are Borel summable at the origin when the frequency vector is either any one-dimensional number or a two-dimensional vector such that the ratio of its components is an irrational number of constant type. In the first case the proof given simplifies that provided in a previous work of ours. We also show that in any dimension $d$, for the existence of a quasi-periodic solution with the same frequency vector as the forcing term, the standard Diophantine condition can be weakened into the Bryuno condition. In all cases, under a suitable positivity condition, the quasi-periodic solution is proved to describe a local attractor.Comment: 10 page

On eigenvalues of the Schr\"odinger operator with an even complex-valued polynomial potential

In this paper, we generalize several results of the article "Analytic continuation of eigenvalues of a quartic oscillator" of A. Eremenko and A. Gabrielov. We consider a family of eigenvalue problems for a Schr\"odinger equation with even polynomial potentials of arbitrary degree d with complex coefficients, and k<(d+2)/2 boundary conditions. We show that the spectral determinant in this case consists of two components, containing even and odd eigenvalues respectively. In the case with k=(d+2)/2 boundary conditions, we show that the corresponding parameter space consists of infinitely many connected components

The size of Wiman-Valiron disks

Wiman-Valiron theory and results of Macintyre about "flat regions" describe the asymptotic behavior of entire functions in certain disks around points of maximum modulus. We estimate the size of these disks for Macintyre's theory from above and below.Comment: 20 page

Markers associated with genomic instability, immunogenicity and immune therapy responsiveness in Metaplastic carcinoma of the breast : Expression of gamma H2AX, pRPA2, P53, PD-L1 and tumor infiltrating lymphocytes in 76 cases

Peer reviewe

Reconstruction of geomagnetic activity and near-Earth interplanetary conditions over the past 167 yr – Part 2: A new reconstruction of the interplanetary magnetic field

We present a new reconstruction of the interplanetary magnetic field (IMF, B) for 1846–2012 with a full analysis of errors, based on the homogeneously constructed IDV(1d)composite of geomagnetic activity presented in Part 1 (Lockwood et al., 2013a). Analysis of the dependence of the commonly used geomagnetic indices on solar wind parameters is presented which helps explain why annual means of interdiurnal range data, such as the new composite, depend only on the IMF with only a very weak influence of the solar wind flow speed. The best results are obtained using a polynomial (rather than a linear) fit of the form B = χ · (IDV(1d) − β)α with best-fit coefficients χ = 3.469, β = 1.393 nT, and α = 0.420. The results are contrasted with the reconstruction of the IMF since 1835 by Svalgaard and Cliver (2010)

Reconstruction of geomagnetic activity and near-Earth interplanetary conditions over the past 167 yr – Part 1: A new geomagnetic data composite

We present a new composite of geomagnetic activity which is designed to be as homogeneous in its construction as possible. This is done by only combining data that, by virtue of the locations of the source observatories used, have similar responses to solar wind and IMF (interplanetary magnetic field) variations. This will enable us (in Part 2, Lockwood et al., 2013a) to use the new index to reconstruct the interplanetary magnetic field, B, back to 1846 with a full analysis of errors. Allowance is made for the effects of secular change in the geomagnetic field. The composite uses interdiurnal variation data from Helsinki for 1845–1890 (inclusive) and 1893–1896 and from Eskdalemuir from 1911 to the present. The gaps are filled using data from the Potsdam (1891–1892 and 1897–1907) and the nearby Seddin observatories (1908–1910) and intercalibration achieved using the Potsdam–Seddin sequence. The new index is termed IDV(1d) because it employs many of the principles of the IDV index derived by Svalgaard and Cliver (2010), inspired by the u index of Bartels (1932); however, we revert to using one-day (1d) means, as employed by Bartels, because the use of near-midnight values in IDV introduces contamination by the substorm current wedge auroral electrojet, giving noise and a dependence on solar wind speed that varies with latitude. The composite is compared with independent, early data from European-sector stations, Greenwich, St Petersburg, Parc St Maur, and Ekaterinburg, as well as the composite u index, compiled from 2–6 stations by Bartels, and the IDV index of Svalgaard and Cliver. Agreement is found to be extremely good in all cases, except two. Firstly, the Greenwich data are shown to have gradually degraded in quality until new instrumentation was installed in 1915. Secondly, we infer that the Bartels u index is increasingly unreliable before about 1886 and overestimates the solar cycle amplitude between 1872 and 1883 and this is amplified in the proxy data used before 1872. This is therefore also true of the IDV index which makes direct use of the u index values